Journal article
3-connected planar spaces uniquely embed in the sphere
In
Transactions of the American Mathematical Society
—
2002, Volume 354, Issue 11, pp. 4585-4595
Abstract
We characterize those locally connected subsets of the sphere that have a unique embedding in the sphere - i.e., those for which every homeomorphism of the subset to itself extends to a homeomorphism of the sphere. This implies that if Ḡ is the closure of an embedding of a 3-connected graph in the sphere such that every 1-way infinite path in G has a unique accumulation point in Ḡ, then Ḡhas a unique embedding in the sphere.
In particular, the standard (or Freudenthal) compactification of a 3-connected planar graph embeds uniquely in the sphere.
| Language: | English |
|---|---|
| Publisher: | American Mathematical Society |
| Year: | 2002 |
| Pages: | 4585-4595 |
| ISSN: | 10886850 and 00029947 |
| Types: | Journal article |
| DOI: | 10.1090/S0002-9947-02-03052-0 |
| ORCIDs: | Thomassen, Carsten |
